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Running Head: Statistics 1 Statistics 2 Zenah Abdulaal Dai Thai Chem

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Running Head: Statistics 1

Statistics 2

Zenah Abdulaal

Dai Thai

Chem. 400

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Classify the following functions as one of the types of functions that we have discussed.

Quadratic Function

Find an equation of the quadratic below:

Find a formula for a cubic function if (−2) = ?(1) = ?(3) = 0 and ?(2) = 8

f(x) = -x^3 + 6x^2 - 13x + 8

Ex 1) Let f(x) = 2x – 3. Find

a) f(–5)

b) f(2)a) f(–5) = 2(-5) – 3

= -10 - 3

= -13

b) f(2) = 2(2) – 3

= 4 - 3

= 1

Ex 2) Use the vertical line test to identify graphs in which y is a function of x.

a) b) c) d)

a) Yes - The vertical line test passes.

b) No - The vertical line test fails.

 

c) Yes - The vertical line test passes.

d) No - The vertical line test fails.

Ex 3) Determine whether the relations are functions:

b) c)) 2? + ?2 = 16 ? = ?2 + 1 ? = ????

a) This is a function because it produces a unique output for each input. The domain is all real numbers, and the range is all real numbers greater than or equal to 4.

b) This is a function because it produces a unique output for each input. The domain is all real numbers, and the range is all real numbers greater than or equal to 1.

c) This is a function because it produces a unique output for each input. The domain is all real numbers, and the range is all real numbers greater than or equal to -1.

Ex 4) Let and? ( ) = ?+1 ?−2 ? ?( ) = ? + 2

Find the domain of each function.

f(x) = (x+1)/(x-2)

Domain of f(x) = {x | x ≠ 2}

g(x) = x + 2

Domain of g(x) = All real numbers

Ex 5) Let f(x) = 2x – 3. State the domain of the function, and find:

 

a) f(–5)

b) f(2)

c) f(a +1)

d) f(x + h)

Domain: x ∈ R

a) f(–5) = 2(-5) – 3 = -13

b) f(2) = 2(2) – 3 = 1

c) f(a + 1) = 2(a + 1) – 3 = 2a + 1 – 3 = 2a – 2

d) f(x + h) = 2(x + h) – 3 = 2x + 2h – 3

Ex 6) Simplify the difference quotient for ? ?+?( )−?(?)

? ? ( ) = 3 − ?2

Piecewise Functions:

? ?+?( )−?(?) = (3 − (?+?)2) − (3 − ?2)

= (3 − ?2 − 2?? − ?2) − (3 − ?2)

= −2?? − ?2

Simplified Difference Quotient:

? ?+?( )−?(?) = −2?? − ?2

 

 

 

Ex 7) Graph the piecewise function ? ( ){?2 − 2? + 1 ??? ? < 2 ? − 1| | ??? ? ≥2

 

For x < 2

f(x) = x2 - 2x + 1

f(0) = 0 - 0 + 1 = 1

f(1) = 1 - 2 + 1 = 0

f(2) = 4 - 4 + 1 = 1

 

For x ≥ 2

f(x) = x - 1

f(2) = 2 - 1 = 1

f(3) = 3 - 1 = 2

f(4) = 4 - 1 = 3

 

x < 2 f(0) f(1) f(2) 1 0 1 x≥2 f(0) f(1) f(2) 1 2 3